Adaptive wavelet method for the Black-Scholes equation of European options

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F16%3A00000522" target="_blank" >RIV/46747885:24510/16:00000522 - isvavai.cz</a>

Výsledek na webu

<a href="http://mme2016.tul.cz/index.php?page=conferenceproceedings" target="_blank" >http://mme2016.tul.cz/index.php?page=conferenceproceedings</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Adaptive wavelet method for the Black-Scholes equation of European options

Popis výsledku v původním jazyce

We use the Black-Scholes model for calculating the price of European put and call options on a basket of assets. The explicit solution of the Black-Scholes equation is known only for some special cases, otherwise it has to be solved numerically. We present the numerical method based on wavelets for an adaptive solution of the Black-Scholes equation. We use several quadratic and cubic spline wavelet bases. Wavelets are very-well known for their compression property. It means that the representation of the solution in a wavelet basis requires a small number of coefficients and the computation of the solution with desired accuracy can be performed with the small number of degrees of freedom. Furthermore, this method enables high-order approximation, the system of linear algebraic equation arising from discretization is well-conditioned and the number of iterations for computing the solution is relatively small. A numerical example is presented for the two-dimensional Black-Scholes equation with real data.

Název v anglickém jazyce

Adaptive wavelet method for the Black-Scholes equation of European options

Popis výsledku anglicky

We use the Black-Scholes model for calculating the price of European put and call options on a basket of assets. The explicit solution of the Black-Scholes equation is known only for some special cases, otherwise it has to be solved numerically. We present the numerical method based on wavelets for an adaptive solution of the Black-Scholes equation. We use several quadratic and cubic spline wavelet bases. Wavelets are very-well known for their compression property. It means that the representation of the solution in a wavelet basis requires a small number of coefficients and the computation of the solution with desired accuracy can be performed with the small number of degrees of freedom. Furthermore, this method enables high-order approximation, the system of linear algebraic equation arising from discretization is well-conditioned and the number of iterations for computing the solution is relatively small. A numerical example is presented for the two-dimensional Black-Scholes equation with real data.

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GA16-09541S" target="_blank" >GA16-09541S: Robustní numerická schémata pro oceňování vybraných opcí za různých tržních podmínek</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

34TH INTERNATIONAL CONFERENCE MATHEMATICAL METHODS IN ECONOMICS (MME 2016)

ISBN

978-80-7494-296-9

ISSN

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e-ISSN

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Počet stran výsledku

6

Strana od-do

120-125

Název nakladatele

TECHNICAL UNIVERSITY LIBEREC, STUDENTSKA 2, LIBEREC, 00000, CZECH REPUBLIC

Místo vydání

Liberec

Místo konání akce

Liberec

Datum konání akce

1. 1. 2016

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

000385239500021